Suppose You Are a Potential College Student That Is Interested

Suppose you are a potential college student that is interested in determining whether it is worthwhile to declare a certain major.In an effort to find the answer,you collect data on 1,247 college graduates who majored in HUMANITIES,SCIENCE,ENGINEERING,or ENGLISH and you estimate the sample regression function (standard errors in parentheses) $$\begin{array} { llllllll } \widehat {\text { Salary }}_{i}=&32,473.81+&5,284.37 \text { GPA }_{4}+&822.56 \text { Male }_{i}+&22,882.43 \text { Science }_{i}\\&( 1,002.97 ) &( 1,323.84 ) & ( 633.85 ) & ( 2,322.43 ) \\\end{array}$$
$$\begin{array} { llllllll } &+ 31,136.74 \text { Engineering } _ { i } + &896.11 \text { English } _ { i } \\&( 5,768.41 )&( 643.20 ) \\\end{array}$$
a)How should you interpret the estimated coefficients for SCIENCE,ENGINEERING,and ENGLISH? Draw a graph and explain.
b)How should you interpret the estimated coefficient for MALE?
c)Are the variables statistical significant at a 5% level?
d)Explain,in as much detail as possible,why the following model is not preferred to the original model. $\begin{aligned}\text { salary }_{i}=&\beta_{0} +\beta_{1} \text { GPA } \\& +\beta_{2} \text { Male }_{i}+\beta_{3} \text { Female }_{i}+\beta_{4} \text { Science }_{i} \\& +\beta_{5} \text { Engineering }_{i}+\beta_{6} \text { English }_{i}\end{aligned}$